Hi, i am very confused when the slope of the indifference curve, it was negative and then it becomes positive when rearranging ? please explain

uo=U(C1)+ \"(C1). 1 + p Assume now that we change consumption in the two periods in such a way that lifetime utility is kept constant. Then we must have: '((02) 1+p where AC, and AC; denote small changes in consumption in the two periods. Hence the slope of the indifference curve is AC2 3" (C1) Ac,' u(ca)/(1+p)' The slope of the mdi'erence curve is the marginal rate of substitution between consumption in the two periods. It is the ratio of the marginal utilities of consumption in the two periods, as seen from period 1. \"'(Cl)ACI + AC2=0: consumption next period - that is, 1 + r. Thus the optimal consumption/savings decision is characterized by the following condition: u'(C1) u' (C2) / (1 + p) =1+r. In order to see the implications of this condition, it is useful to divide by 1 + p on both sides: u (C) 1+r u' (C2) 1+ p If the subjective discount rate is equal to the market rate of interest, the right- hand side is equal to unity, which means that the left-hand side must also be equal to unity. This can only be true if consumption is equal in the two periods. Thus we see that, if the subjective discount rate is equal to the market rate of inter- est, the consumer will plan for consumption to be constant over time. This is a consequence of the preference for smooth consumption. Independent of how much income the individual gets in different periods, she wants to save (or bor- row) so as to smooth consumption over time. This is illustrated in Fig. 4.5 where the tangency points illustrate optimal consumption choice for two consumers with different incomes in the two periods. Two different consumers with different incomes in the two periods, here given by points A and B, will consume different amounts, but each will consume the same amount in both periods